P-Values for Composite Null Models

• Activity Number: 669
• Type: Invited
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Memorial
• Author(s): James M. Robins*
• Companies: Harvard University
• Keywords: p-value ; posterior predictive ; model adequacy

Abstract

In 1999, Susie Bayarri and Jim Berger proposed two new Bayesian p-values : the conditional predictive p-value and the partial posterior predictive p-value. They showed, in a number of canonical examples, that, for checking the adequacy of a parametric model, these p-values were much superior to the posterior predictive p-value of Guttman (1967) and Rubin (1984). They restricted themselves to examples in which it was possible to obtain the exact distribution of these p-values. Robins, van der Vaart ,and Ventura (2000) studied the large sample properties of these various p-values. They found the new p-values to have an asymptotic uniform distribution; in contrast they found that the posterior predictive p-value could be extremely conservative, vastly diminishing the power to detect a mis-specified model. It is remarkable that, in proposing these new p-values motivated through Bayesian arguments, Bayarri and Berger solved the frequentist problem of constructing an asymptotically uniformly distributed p-value based on any test statistic with a limiting normal distribution. Even more remarkable is that the obvious non-Bayesian competitors failed to be uniform.